Physics swing question?

Question

a swing is made from a rope that tollerates a max tension of 8.00^2N without breaking. initially the swing hangs vertically. it is then pulled back at 50 degrees to the vertical and released from rest. what is the maximum weight for a person to ride the swing

Answer 1

♣max centripetal force is F=m*v^2/R, where R is length of the rope, v is max speed of the swing;

♣when pulled back at angle b=50° you get pot energy E=mg*(R-R*cos(b)) – draw a pic! This corresponds to kin energy in the lowest position E=0.5*m*v^2;  

♦ E=E; therefore mg*(R-R*cos(b)) =0.5*m*v^2, hence

mv^2/R =2mg*(1-cosb), which exactly corresponds to F above!

Thus you get F = 2mg*(1-cosb), and taking your weight into account we get

800N =2mg*(1-cosb) + mg, hence your mass is

m= (800/g)/ (2*(1-cosb) +1) = 47.6kg;

♠ last week we decided to invite you to Physics Department of Science Academy; will you take the position?